Question

The value of acceleration due to gravity is ` 980 cm s^(-2)`. What will be its value if the unit of length is kilometer and that of time is minute?

Answer 1

Correct Answer - `3.53`
Dimension of acceleration due to gravity is `[LT^(-2)]`.
In CGS system , Let `L_(1)` and `T_(1)` represent length and time measured in cm and second , respectively . Let `n_(2)` be the value of acceleration due to gravity in the new system . The length `L_(2)` and time `T_(2)` are measured in kilometer and minute, respectively.
Now `n_(1) [ L_(1) T_(1)^(-2)] = n_(2) [ L_(2) T_(2)^(-2)]`
or ` n_(2) = n_(1) [(L_(1))/(L_(2))] [(T_(1))/(T_(2))]^(-2)`
`= 980 [(1)/( 10^(5))] [(1)/( 60)]^(-2) = ( 980 xx 60 xx 60)/( 10^(5)) = 3.53`